Unformatted text preview: sets are VI, . .. , vm and vm+b . .. , Vm+ n ' the 1 1 0 0 adjacency matrix is 1 1 0 0 3. (a) [BB] The (3,5) entry of A3 is the number of walks of length 3 from C to E and, hence, equals 5. The (2,2) entry of A3 is the number of walks oflength 3 from B to itself, hence, equals 2. (b) The (3,5) entry of A3 equals 2. The (2,2) entry of A3 equals 4. 4. [BB] Each 1 represents an edge. Each edge ViVj contributes two l's to the matrix, in positions (i,j) and (j, i). The number of l's is twice the number of edges. 5. The ith entry on the diagonal of A3 is the number of walks of length 3 from Vi to itself. However, a closed walk of length 3 in a graph must give a triangle. Every triangle can be walked in exactly two different directions. Hence, the number of walks of length 3 is twice the number of triangles....
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- Summer '10
- Graph Theory, Walking, Glossary of graph theory, adjacency matrix, Adjacency list